Crack tip fields in soft elastic solids subjected to large quasi-static deformation — A review

Abstract

We review analytical solutions for the asymptotic deformation and stress fields near the tip of a crack in soft elastic solids. These solutions are based on finite strain elastostatics and hyperelastic material models, and exhibit significantly different characteristics than the classical crack tip field solutions in linear elastic fracture mechanics. Specifically, we summarize some available finite strain crack tip solutions for two dimensional cracks, namely that plane strain, plane stress, and anti-plane shear cracks in a certain class of homogeneous materials. Interface cracks between soft elastic solids and a rigid substrate are also discussed. We focus on incompressible material models with various degrees of strain stiffening effect such as generalized neo-Hookean model, exponentially hardening model and Gent model. We also explored the physical implications of the crack tip fields, and highlighted pitfalls in the applications of these solutions, particularly the J-integral and the distribution of true stress in the deformed configuration which have not been discussed in the literature.